Adjusted Even-Strength Plus-minus 1968-2008

I've studied correlations between ES icetime and ESGF+ESGA and they don't necessarily correspond very well, perhaps especially regarding forwards. For example, during 2002-03, I guy like Kowalchuk (who had a reputation as an offensive minded player) had about 1.5 times more ESGF+ESGA played than the average player.
So here we thus have our first bias. ESGF=60 and ESGA=50, will give higher "ice time" than ESGF=50 and ESGA=40, even if real ice time is the same. ?

I'm not sure ice time is so important. If a player is on ice for a much higher % of ES GF+GA than his % of his ice time, that's okay. If he's able to perform at or above the GF/GA ratio of the team as a whole, then the more volume the better for the team. If he's at a worse GF/GA level, then the high volume will negatively effect the player portion of the metric even more.

Quote:

Originally Posted by plusandminus

I'm a bit against dividing ESGF by ESGA. As i wrote in another reply some day ago, I think there are better ways to do it. To use the above example, I would say that 60-50 and 50-40 is equally good, despite the latter one getting a slightly higher ratio (if I understand you right).

I don't know why you are so against calculating GF/GA ratios. They shouldn't be used randomly, but in this case they are the primary basis of the pythagorean win% calculation, so of great importance.

Whether 60/50 or 50/40 is better may depend most on context (all other things being equal). On a bad team, the extra 10/10 might be helpful, while on a good team, it may be hurtful.

Quote:

Originally Posted by plusandminus

I googled, and according to wikipedia I got the impression that rather 1.8 was the "right exponent", at least in baseball?

Wouldn't shootout goals be excluded from the stats?

I saw more than one study for hockey. If 1.8 or whatever number is deemed a solid number, I have not attachment to 2.0 as exponent. It does vary by sport though, I think mainly due to differing scoring levels.

Quote:

Originally Posted by plusandminus

That's 94-38 = +56 with Forsberg. And 84-87 = -3 without.
Not only did he have the league's by far best ES+/-, and scored the highest amount of ESpts, on a team that without him (and the guys who were on the ice with him) had negative +/-.

Adding ESGF+ESGA, we get 94+38=132 for him. 178+125=303 for the team.
That's an "ice time" of 43.56 % according to ESGF+ESGA.

I got 43.56 %, so at least one of us (perhaps I) may be wrong.

In reality, the correct answer seems to be 28.84 %. (if my data is correct)
So, the estimated percentage is about 1.5 times higher.

You are correct. I have realized yet another error in this hastily put together study. I had calculated player's % of team's GF and GA separately and then summed them, instead of summing them before calculating the player's % of team. I came up with this idea a couple days ago and used some existing player data for the basis of most of the calculations, but that doesn't excuse my sloppiness.

Nice job of checking my math!

Quote:

Originally Posted by plusandminus

And I think three players with identical EStime, having ESGF-ESGA of 40-40 and 30-30 and 20-20 contributes equally much.

Quote:

Originally Posted by plusandminus

It would be interesting to this stat listed for all the players on a team.
(I can do it myself, but not right now.)
With the risk of being called an idiot, does the sum of all players equal 100??

I don't have calculations for an entire team. I think the totals would not exactly balance, but should not be way off either.

The total for all players on the team should be somewhere around:

5 * 82 * (team's ES pythagorean win%)

note: 5 is number of skaters per goal

For a team with equal ES GF and GA, should be ~205 "ES wins"

Quote:

Originally Posted by plusandminus

Pittsburgh were a bit special that year, starting the season with some very good players, just to see them drop off one by one. So Mario's stats sank deeper and deeper during the season. (If I remember right.)

Yeah, Pittsburgh was real "special" for a few years there post-Jagr.

In '94 and '96, Lemieux's R-On was slightly less than R-Off, although a big reason for that is Jagr being such a large part of the R-Off. His R-On/R-Off is great in '97 (1.97) and very good in 2001 (1.39), but a lot of that was due to those being the 1.5 seasons he played with Jagr at even strength. After that, he was mostly weak.

Quote:

Originally Posted by plusandminus

A thought I have, is that one might want to seperate forwards and defencemen, since they may not be easily comparable.

An additional way of improving (or not) the method, could be to include ESpts in the calculations, to estimate how much different players contributed to their ESGF. Now I'm mainly thinking of doing it for forwards, to help seperate the offensive contributions of linemates, although it might be useful to apply (perhaps in a differnt form) to defencemen as well. To do something similar for ESGA would of course be basically impossible (unless one apply an assumption like "defencemen being more responsible for ESGA, while forwards being more responsible for ESGF").

Yes, separating forwards and defensemen is one possibilty. Would rather not do that... and what about players like Coffey that could almost be classified as either? I like using a player's ES points as a % of ESGF, but this requires even more data and doesn't address ESGA. I think the latter is probably the better way to go, or it may be better to just live with a "pure" but flawed metric.

Quote:

Originally Posted by plusandminus

Finally, which you likely are aware of, this stat only tells us about players' contributions during ES. So the "rankings" here are ES only.
Creating similar stats for PP and SH would rank players differently.
For example. While Forsberg had "much better" ES stats than Naslund in 2002-03, Naslund had better PP stats.

Of course this, like adjusted plus-minus, isn't an all-encompassing metric. It's meant to shed light on even strength value. Still, about ~75% of goals occur at even strength and it's even strength play that leads to penalties, so ES play is crucial to overall value.

I don't know why you are so against calculating GF/GA ratios. They shouldn't be used randomly, but in this case they are the primary basis of the pythagorean win% calculation, so of great importance.

I'll try to explain.

If I was asked to rank the following seasonal ES stats for players, without paying any attention at all to context, I would rank them as follow (with a tie for 2nd best):

GF-GA

GD

GF/GA

GF+GA

(GF/GA)*(GF+GA)

72-50

+22

1.440

112

161.28

60-40

+20

1.500

100

150

40-20

+20

2.000

60

120

45-30

+15

1.500

75

112.5

7- 4

+ 3

1.750

11

19.25

3- 1

+ 2

3.000

4

12

GD=GF-GA (goal difference). GS=GF+GA (goal sum).

Comments:
1. The guy with a GF/GA of 3.000 looks far too good compared to the others.
2. The lower numbers, the more extreme GF/GA. (It's a bit like pts per game. The fewer games played, the more extreme points per game.)

That's why I generally think one should be careful with using GF/GA.

Also:
3. Player ice time share during ES vary a lot between players. So does the amount time the player was not on the ice. No matter if one use real ice times, or take GF+GA, the differences are big.
4. Thus, when comparing "with" and "without", we would be comparing for example a GF/GA based on very low numbers, with a GF/GA based on very high numbers.

I'm not convinced yet regarding how good the win formula, and other formulas are at handling the things I mentioned above. Maybe they are great.

Quote:

Originally Posted by Czech Your Math

I'm not sure ice time is so important. If a player is on ice for a much higher % of ES GF+GA than his % of his ice time, that's okay. If he's able to perform at or above the GF/GA ratio of the team as a whole, then the more volume the better for the team. If he's at a worse GF/GA level, then the high volume will negatively effect the player portion of the metric even more.

The above seems based a lot on GF/GA, and I think GF/GA can "lie".

Let's say we have a 2-3 result without player on ice (GF/GA=0.400).
Player on ice doing 5-3 will make his team win 7-6, despite GF/GA=1.667.
Player on ice doing 2-1will only make his team draw 4-4, despite GF/GA of 2.00.

As I said, maybe the win formula and other formulas have methods to guard for such contradictions.

Quote:

Whether 60/50 or 50/40 is better may depend most on context (all other things being equal). On a bad team, the extra 10/10 might be helpful, while on a good team, it may be hurtful.

By themselves, I think both are equal. Context may make one look better, but I'm not sure GF/GA is the best way to determine that.
I may be wrong.

If I was asked to rank the following seasonal ES stats for players, without paying any attention at all to context, I would rank them as follow (with a tie for 2nd best):

GF-GA

GD

GF/GA

GF+GA

(GF/GA)*(GF+GA)

72-50

+22

1.440

112

161.28

60-40

+20

1.500

100

150

40-20

+20

2.000

60

120

45-30

+15

1.500

75

112.5

7- 4

+ 3

1.750

11

19.25

3- 1

+ 2

3.000

4

12

GD=GF-GA (goal difference). GS=GF+GA (goal sum).

Comments:
1. The guy with a GF/GA of 3.000 looks far too good compared to the others.
2. The lower numbers, the more extreme GF/GA. (It's a bit like pts per game. The fewer games played, the more extreme points per game.)

That's why I generally think one should be careful with using GF/GA.

The metric I've been tinkering with does not use any formula akin to (GF/GA)*(GF+GA). Neither does Overpass' adjusted plus-minus. Also, I agree that small sample sizes tend to lead to skewed results. That is why taking the best X seasons or career numbers are going to be more reliable for almost any metric.

In your 60/40 vs. 40/20 example, context is very important. First, it tells you in what environment the data was created. Second, it tells you what impact the player's performance is going to have. Since one player has 20/20 more than the other, if the R-Off of his team was > 1.0, then his performance did not help his team, while if it was < 1.0 it did help his team.

Quote:

Originally Posted by plusandminus

Also:
3. Player ice time share during ES vary a lot between players. So does the amount time the player was not on the ice. No matter if one use real ice times, or take GF+GA, the differences are big.
4. Thus, when comparing "with" and "without", we would be comparing for example a GF/GA based on very low numbers, with a GF/GA based on very high numbers.

I'm not convinced yet regarding how good the win formula, and other formulas are at handling the things I mentioned above. Maybe they are great.

Again, that's why need multiple seasons to have any real solid data.

Maybe I should focus more or solely on the player's portion of the formula. I came up with the distribution of team's ES wins while thinking of some way to address Overpass' concern that players on great teams are hampered by the team's strong R-OFF. Honestly, getting credit for "just showing up" is not that great, although it's actually "playing a lot for great teams", and usually it's very good players who get lots of ice time over many years on great teams.

The player's portion is calculated by deducting his ES goals for/against from the team totals. The better the ratio and the more goals he was on ice for, the more impact it will have on the estimated win% differential, but it's more complex than multiplying the GF/GA ratio by the sum of ES GF + GA.

Quote:

Originally Posted by plusandminus

The above seems based a lot on GF/GA, and I think GF/GA can "lie".

Let's say we have a 2-3 result without player on ice (GF/GA=0.400).
Player on ice doing 5-3 will make his team win 7-6, despite GF/GA=1.667.
Player on ice doing 2-1will only make his team draw 4-4, despite GF/GA of 2.00.

As I said, maybe the win formula and other formulas have methods to guard for such contradictions.

All stats can "lie", 76% of statisticians can attest to that.

I'm not using GF/GA ratio as an absolute metric. In referring to Overpass' adjusted plus-minus, I do think R-ON/R-OFF is a valuable metric. It tells you in % terms how much more effective the team was with that player on the ice than without him on the ice, and that's a valuable piece of information.

Quote:

Originally Posted by plusandminus

By themselves, I think both are equal. Context may make one look better, but I'm not sure GF/GA is the best way to determine that.
I may be wrong.

They are similar, but not equal in most cases. An extra 10 GF and 10 GA is outstanding on the '75 Capitals and rather weak on a dynasty team.

It seems I got a bit misunderstood when I included a (GF/GA)*(GF+GA) column. That column was just there as an example of what results it would show. It was the other columns that were the important ones. Below I have deleted that column.

GF-GA

GD

GF/GA

GF+GA

72-50

+22

1.440

112

60-40

+20

1.500

100

40-20

+20

2.000

60

45-30

+15

1.500

75

7- 4

+ 3

1.750

11

3- 1

+ 2

3.000

4

GD=GF-GA (goal difference). GS=GF+GA (goal sum).

Quote:

Originally Posted by Czech Your Math

Also, I agree that small sample sizes tend to lead to skewed results. That is why taking the best X seasons or career numbers are going to be more reliable for almost any metric.

Yes. But has it been tested out how much more reliable?
I may try to examine that a bit more.

I also intend to look at game by game to see just what ES result the player had in the game ("with"), and what ES result the team had with him off ice ("without").
I know this can only be done for recent seasons, unless one wants to rely on estimated ES stats, but I still think it would be interesting to see what results it will produce. I'll get GP W D L GF-GA Pts for the players ("with") and for "without" them, and can then compare the two.

Quote:

In your 60/40 vs. 40/20 example, context is very important. First, it tells you in what environment the data was created. Second, it tells you what impact the player's performance is going to have. Since one player has 20/20 more than the other, if the R-Off of his team was > 1.0, then his performance did not help his team, while if it was < 1.0 it did help his team.

I understand your example here. But I so far don't like GF/GA to be used, for reasons I have tried to put forward.

Quote:

The player's portion is calculated by deducting his ES goals for/against from the team totals. The better the ratio and the more goals he was on ice for, the more impact it will have on the estimated win% differential

I understand that. That's what I call "with" and "without". And "with" may be unproportional compared to "without".

I will experiment a bit on my own to see how much it may affect the results.

Quote:

All stats can "lie", 76% of statisticians can attest to that.

That was a funny statement.

Quote:

They are similar, but not equal in most cases. An extra 10 GF and 10 GA is outstanding on the '75 Capitals and rather weak on a dynasty team.

IYes. But has it been tested out how much more reliable?
I may try to examine that a bit more.

The "pure" part is the player portion. Taking the differential of the estimated pythagorean win% based on performance. What part of that do you disagree with? I understand the exponent is a bit difficult to pinpoint, but I don't think it makes much difference when comparing players, since all would be affected similarly.

The assignment of some portion of the team's success based is somewhat arbitrary and perhaps not necessary at all.

Quote:

Originally Posted by plusandminus

I also intend to look at game by game to see just what ES result the player had in the game ("with"), and what ES result the team had with him off ice ("without").
I know this can only be done for recent seasons, unless one wants to rely on estimated ES stats, but I still think it would be interesting to see what results it will produce. I'll get GP W D L GF-GA Pts for the players ("with") and for "without" them, and can then compare the two.

Are you talking about ES data in games the player did not play? If you have that data, it would be interesting. However, if that's what you mean, why not just look at total results (record, GF, GA). I've calculated the actual vs. expected win% for a few players, and could also calculated expected win % using pythagorean based on GF/GA.

If you're bringing ice time into the picture, I don't consider that very important in comparison.

Quote:

Originally Posted by plusandminus

I understand that. That's what I call "with" and "without". And "with" may be unproportional compared to "without".

I will experiment a bit on my own to see how much it may affect the results.

With and without, yes it's a fairly simple concept.
I don't understand what you mean by unproportional.

I think only games where the player were on the ice on a goal (no matter what type of goal) are counted. The missing games are all 0-0 for the player.
(Better would be to include all the games the player participated in, but unfortunately that informations seems to be depleted because of a disk crash several years ago.)

Just an example.

Team

Pos

Name

Game

+/-

x+/-

Pts

xPts

totPts

Pts-x

tot-x

W

D

L

xW

xD

xL

tW

tD

tL

COL

C

PETER FORSBERG

68

55

1

97

61

91

36

30

40

17

11

21

19

28

39

13

16

COL

R

MILAN HEJDUK

73

49

-1

98

72

94

26

22

37

24

12

27

18

28

41

12

20

LA

R

ZIGMUND PALFFY

71

24

-26

86

53

71

33

18

30

26

15

17

19

35

25

21

25

DAL

R

JERE LEHTINEN

64

33

21

89

72

86

17

14

34

21

9

27

18

19

34

18

12

DAL

D

DERIAN HATCHER

75

27

27

90

85

99

5

14

36

18

21

32

21

22

40

19

16

TB

R

MARTIN ST. LOUIS

70

7

-19

78

54

67

24

13

29

20

21

16

22

32

25

17

28

COL

L

ALEX TANGUAY

69

38

10

88

76

89

12

13

35

18

16

31

14

24

38

13

18

DET

D

NICKLAS LIDSTROM

80

36

2

95

84

97

11

13

37

21

22

31

22

27

40

17

23

NJ

R

JAMIE LANGENBRUNNER

59

16

14

66

62

75

4

13

25

16

18

22

18

19

32

11

16

How to read the table:
Forsberg was +55 during ES, without him Colorado was +1 during ES. Forsberg was 40-11-17 (W-L-D) during ES. That would have resulted in 97 pts in 68 games. It seems he (and his units) helped getting Colorado 30 more "ES points" (91 instead of 61). Again, everything is ES only, and only games where player where on the ice on a goal is counted.

Sorted another way, it would look like:

Team

Pos

Name

Game

+/-

x+/-

Pts

xPts

totPts

Pts-x

tot-x

W

D

L

xW

xD

xL

totW

totD

totL

CBJ

R

DAVID VYBORNY

59

15

-63

71

32

37

39

5

24

23

12

9

14

36

14

9

36

COL

C

PETER FORSBERG

68

55

1

97

61

91

36

30

40

17

11

21

19

28

39

13

16

LA

R

ZIGMUND PALFFY

71

24

-26

86

53

71

33

18

30

26

15

17

19

35

25

21

25

CAR

D

SEAN HILL

66

5

-44

69

42

52

27

10

22

25

19

11

20

35

20

12

34

COL

R

MILAN HEJDUK

73

49

-1

98

72

94

26

22

37

24

12

27

18

28

41

12

20

MTL

D

ANDREI MARKOV

71

18

-23

88

62

66

26

4

32

24

15

20

22

29

25

16

30

TB

R

MARTIN ST. LOUIS

70

7

-19

78

54

67

24

13

29

20

21

16

22

32

25

17

28

CBJ

L

GEOFF SANDERSON

71

-1

-56

70

47

42

23

-5

20

30

21

13

21

37

14

14

43

LA

L

ALEXANDER FROLOV

58

16

-16

69

48

59

21

11

28

13

17

19

10

29

22

15

21

TB

C

VACLAV PROSPAL

70

7

-21

81

60

67

21

7

27

27

16

16

28

26

25

17

28

The difference between Vyborny on the ice, and Vyborny off the ice, is hugh. +15 with, -63 without. With him, 71 points in 59 games, without him only 32 points in 59 games. His contributions however only helped Columbus get 5 more points more than if he had been +/- 0 in every game. Same data and limitations as above.

Just an example. Just intended as something to add to the debate.
I know important stats are missing for older data. Again, just an example.

Pts, xPts and totPts can be used to tell us about pts per game:

Team

Pos

Name

Game

ES+/-

xES+/-

Pts

xPts

totPts

Pts-xPts

totPts-xPts

ATL

C

KAMIL PIROS

2

4

-2

2.000

0.000

1.500

2.000

1.500

WAS

D

MICHAEL FARRELL

1

1

-1

2.000

0.000

1.000

2.000

1.000

NAS

D

TOMAS KLOUCEK

1

1

-1

2.000

0.000

1.000

2.000

1.000

VAN

R

PAT KAVANAGH

2

2

-2

2.000

0.000

1.000

2.000

1.000

I personally find totals more useful.

Results does seem more useful if for example only taking those with minimum of 41 games:

Team

Pos

Name

Game

ES+/-

xES+/-

Pts

xPts

totPts

Pts-xPts

totPts-xPts

COL

C

PETER FORSBERG

68

55

1

1.426

0.897

1.338

0.529

0.441

COL

R

MILAN HEJDUK

73

49

-1

1.342

0.986

1.288

0.356

0.301

LA

R

ZIGMUND PALFFY

71

24

-26

1.211

0.746

1.000

0.465

0.254

NJ

R

JAMIE LANGENBRUNNER

59

16

14

1.119

1.051

1.271

0.068

0.220

DAL

R

JERE LEHTINEN

64

33

21

1.391

1.125

1.344

0.266

0.219

PHO

L

LADISLAV NAGY

62

24

-10

1.210

0.952

1.145

0.258

0.194

LA

L

ALEXANDER FROLOV

58

16

-16

1.190

0.828

1.017

0.362

0.190

COL

L

ALEX TANGUAY

69

38

10

1.275

1.101

1.290

0.174

0.188

DAL

D

DERIAN HATCHER

75

27

27

1.200

1.133

1.320

0.067

0.187

STL

R

ERIC BOGUNIECKI

43

11

-10

1.186

0.721

0.907

0.465

0.186

I prefer the totals (first two tables in this post) more than the averages.

Perhaps, though, "Pts as a total" might be wisely combined with "xPts per game".

Dividing, or dividing with square root, would give:

Team

Pos

Name

Game

ES+/-

xES+/-

Pts

PtsG

xPts

totPts

totPts2

totPts3

COL

C

PETER FORSBERG

68

55

1

97

1.426

0.897

1.338

108.13114

102.41445

LA

R

ZIGMUND PALFFY

71

24

-26

86

1.211

0.746

1.000

115.20754

99.538178

COL

R

MILAN HEJDUK

73

49

-1

98

1.342

0.986

1.288

99.361111

98.678208

CBJ

R

DAVID VYBORNY

59

15

-63

71

1.203

0.542

0.627

130.90625

96.407176

MTL

D

ANDREI MARKOV

71

18

-23

88

1.239

0.873

0.930

100.7741

94.170744

STL

D

AL MACINNIS

78

19

-3

92

1.179

0.962

1.038

95.680000

93.821959

DET

D

NICKLAS LIDSTROM

80

36

2

95

1.188

1.050

1.212

90.476190

92.710506

TB

C

BRAD RICHARDS

75

8

-17

82

1.093

0.840

0.973

97.619047

89.469334

STL

D

BARRET JACKMAN

74

17

-6

87

1.176

0.959

1.014

90.676056

88.819012

TB

R

MARTIN ST. LOUIS

70

7

-19

78

1.114

0.771

0.957

101.11111

88.806906

NYR

C

ERIC LINDROS

75

15

-3

87

1.160

0.960

1.053

90.625

88.794003

WAS

D

SERGEI GONCHAR

75

17

-5

86

1.147

0.960

1.040

89.583333

87.773382

TotPts2=Pts/(xPts/Games). TotPts3=Pts/sqrt(xPts/Games)

I'm not saying this last table above gives the best results, just that it uses another way of combining "with" and "without".

Maybe the results of the "win formula" and/or overpass' method would be fairly similar (or not).

I think this is an interesting way to look at things. I know one needs some data that are not available for "old" seasons, but still. And the results here may be compared to the other methods in this thread, to see how they correspond to each other.

Edit:
The above should basically work for all eras, no matter how high or low scoring. Only thing to adjust for would be GP per season (for teams, i.e. 82 nowadays, 80 during Gretzy's prime).
It should also take care of injuries. If a player misses a game, he simply gets 0 pts for that game. It should be very easy to aggregate different seasons to get career totals (if it wasn't for necessary data missing).

OK.
I've studied correlations between ES icetime and ESGF+ESGA and they don't necessarily correspond very well, perhaps especially regarding forwards. For example, during 2002-03, I guy like Kowalchuk (who had a reputation as an offensive minded player) had about 1.5 times more ESGF+ESGA played than the average player.
So here we thus have our first bias. ESGF=60 and ESGA=50, will give higher "ice time" than ESGF=50 and ESGA=40, even if real ice time is the same. ?

I'm surprised CYM didn't mention/ask this, but... did you mean he had about 1.5 times the "average" player? or the average of his own team? there are only so many minutes to go around, and I find it unlikely that he would be that far off of his own team's average. If you compare him to another team, sure, his icetime figures would look wonky. but that's not what a model that uses GF & GA to calculate icetime does.

Also, Kovalchuk is about the most extreme example of a "high risk, high reward" type player. Watching the guy play it is clear he is going to cause both more goals for and more goals against while on the ice. If there was ever a player who would be an outlier whose GF/GA figures might cause an estimation model to lie, it would be him. With that said, that's no reason to throw out such a model.

Quote:

If I was asked to rank the following seasonal ES stats for players, without paying any attention at all to context, I would rank them as follow (with a tie for 2nd best):

Comments:
1. The guy with a GF/GA of 3.000 looks far too good compared to the others.
2. The lower numbers, the more extreme GF/GA. (It's a bit like pts per game. The fewer games played, the more extreme points per game.)

That's why I generally think one should be careful with using GF/GA.

I have an even more compelling reason to throw out the bottom player - any calculation done on him would be based on an obscenely low number of game situations. It's a poor sample size and is practically meaningless. Of course, if it got further in the season and he was 40-13, then we'd have something to talk about, and whether he was outperforming the 72-50 player would be a worthy question to ask.

I'm surprised CYM didn't mention/ask this, but... did you mean he had about 1.5 times the "average" player? or the average of his own team? there are only so many minutes to go around, and I find it unlikely that he would be that far off of his own team's average. If you compare him to another team, sure, his icetime figures would look wonky. but that's not what a model that uses GF & GA to calculate icetime does.

Thanks for asking. I compare only with his team's totals.

Below are what it looks like. I have only included players with GF+GA >= 20. (Expect even larger differences for the other players.)
I think the raw data I assembled and corrected should be near 100 % correct.
The rightmost column shows GF+GA per 60 minutes. I have divided all those values by league average, to make it easier to compare.

Highest:

Team

Name

pos

ESTOI

EStoi%

ESGFGA%

diff

ESGFGA

normESGFGAper60min

CAR

BRUNO ST. JACQUES

D

297

0.081

0.138

0.057

35

1.577

CHI

BURKE HENRY

D

250

0.065

0.094

0.029

29

1.552

ATL

ILYA KOVALCHUK

F

1153

0.305

0.379

0.074

130

1.509

NYR

REM MURRAY

F

398

0.105

0.155

0.050

44

1.479

EDM

MIKE COMRIE

F

910

0.241

0.328

0.086

100

1.470

CHI

ERIC DAZE

F

722

0.188

0.257

0.070

79

1.464

LA

ADAM DEADMARSH

F

265

0.071

0.106

0.035

29

1.464

COL

PETER FORSBERG

F

1091

0.288

0.419

0.131

119

1.459

BOS

JOE THORNTON

F

1285

0.340

0.433

0.093

140

1.458

ATL

KIRILL SAFRONOV

D

414

0.110

0.131

0.022

45

1.454

TOR

ALEXANDER MOGILNY

F

943

0.258

0.348

0.090

102

1.447

TOR

KAREL PILAR

D

245

0.067

0.089

0.022

26

1.420

BOS

GLEN MURRAY

F

1400

0.371

0.458

0.087

148

1.414

ATL

DANY HEATLEY

F

1164

0.308

0.359

0.051

123

1.414

NYI

ROMAN HAMRLIK

D

1281

0.355

0.460

0.106

134

1.400

PIT

MARIO LEMIEUX

F

1082

0.286

0.387

0.101

113

1.397

MTL

NIKLAS SUNDSTROM

F

384

0.098

0.129

0.031

40

1.394

PHO

LANDON WILSON

F

328

0.089

0.125

0.036

34

1.387

SJ

NICHOLAS DIMITRAKOS

F

244

0.065

0.089

0.023

25

1.371

BOS

MIKE KNUBLE

F

1061

0.281

0.334

0.053

108

1.362

Lowest:

Team

Name

pos

ESTOI

EStoi%

ESGFGA%

diff

ESGFGA

normESGFGAper60min

WAS

BRIAN SUTHERBY

F

554

0.146

0.096

-0.05

27

0.652

PIT

IAN MORAN

F

1053

0.278

0.175

-0.10

51

0.648

CGY

STEVE BEGIN

F

436

0.118

0.078

-0.04

21

0.644

STL

TYSON NASH

F

532

0.142

0.087

-0.05

25

0.629

TOR

RICHARD JACKMAN

D

535

0.146

0.085

-0.06

25

0.625

FLA

IGOR ULANOV

D

823

0.215

0.146

-0.07

38

0.618

MIN

JASON MARSHALL

F

462

0.119

0.084

-0.04

21

0.608

TB

ALEXANDER SVITOV

F

511

0.132

0.083

-0.05

23

0.602

CAR

JAROSLAV SVOBODA

F

549

0.150

0.095

-0.05

24

0.585

TOR

PAUL HEALEY

F

458

0.125

0.068

-0.06

20

0.584

BUF

VACLAV VARADA

F

525

0.139

0.082

-0.06

22

0.561

CGY

STEVE MONTADOR

D

627

0.170

0.096

-0.07

26

0.555

STL

SHJON PODEIN

F

540

0.144

0.073

-0.07

21

0.520

COL

SERGE AUBIN

F

700

0.185

0.095

-0.09

27

0.516

PIT

IAN MORAN

D

1053

0.278

0.134

-0.14

39

0.496

Biggest differences between real ES%, and ES% estimated by GF+GA:

Team

Name

pos

ESTOI

EStoi%

ESGFGA%

diff

ESGFGA

normESGFGAper60min

PIT

IAN MORAN

D

1053

0.278

0.134

-0.14

39

0.496

COL

PETER FORSBERG

F

1091

0.288

0.419

0.131

119

1.459

NYI

MATTIAS TIMANDER

D

1159

0.321

0.213

-0.11

62

0.716

NYI

ROMAN HAMRLIK

D

1281

0.355

0.460

0.106

134

1.400

PIT

MARIO LEMIEUX

F

1082

0.286

0.387

0.101

113

1.397

PHO

OSSI VAANANEN

D

1056

0.287

0.192

-0.10

52

0.659

PIT

IAN MORAN

F

1053

0.278

0.175

-0.10

51

0.648

STL

PAVOL DEMITRA

F

1151

0.308

0.406

0.098

116

1.348

TB

VINCENT LECAVALIER

F

1134

0.293

0.390

0.097

108

1.274

BOS

JOE THORNTON

F

1285

0.340

0.433

0.093

140

1.458

WAS

SERGEI GONCHAR

D

1584

0.417

0.509

0.092

143

1.208

TOR

ALEXANDER MOGILNY

F

943

0.258

0.348

0.090

102

1.447

CGY

STEPHANE YELLE

F

1054

0.285

0.200

-0.09

54

0.686

COL

SERGE AUBIN

F

700

0.185

0.095

-0.09

27

0.516

BOS

GLEN MURRAY

F

1400

0.371

0.458

0.087

148

1.414

EDM

MIKE COMRIE

F

910

0.241

0.328

0.086

100

1.470

COL

MILAN HEJDUK

F

1219

0.322

0.405

0.083

115

1.262

TB

MARTIN ST. LOUIS

F

1123

0.290

0.372

0.082

103

1.227

FLA

OLLI JOKINEN

F

1168

0.305

0.385

0.080

100

1.146

BOS

SEAN O'DONNELL

D

1150

0.305

0.229

-0.08

74

0.861

VAN

TODD BERTUZZI

F

1223

0.334

0.413

0.079

117

1.280

DET

MATHIEU DANDENAULT

D

1203

0.314

0.392

0.078

122

1.357

PHO

PAUL MARA

D

1129

0.307

0.384

0.077

104

1.233

FLA

IVAN NOVOSELTSEV

F

960

0.250

0.327

0.077

85

1.185

MIN

MARIAN GABORIK

F

1078

0.278

0.355

0.077

89

1.105

ATL

ILYA KOVALCHUK

F

1153

0.305

0.379

0.074

130

1.509

This makes, in my opinion, GF+GA a bit unreliable when using it to determine ice time. Maybe there are steps involved in the calculations that takes care of that, so that it really doesn't matter that much. But I felt a need to point it out.

Quote:

Also, Kovalchuk is about the most extreme example of a "high risk, high reward" type player. Watching the guy play it is clear he is going to cause both more goals for and more goals against while on the ice. If there was ever a player who would be an outlier whose GF/GA figures might cause an estimation model to lie, it would be him. With that said, that's no reason to throw out such a model.

Agree about Kowalchuk. But there were lots of other players like him. And plenty of the opposite kind too, i.e. players with "low risk getting scored on, but also low risk for their opponents to be scored on".

Quote:

I have an even more compelling reason to throw out the bottom player - any calculation done on him would be based on an obscenely low number of game situations. It's a poor sample size and is practically meaningless. Of course, if it got further in the season and he was 40-13, then we'd have something to talk about, and whether he was outperforming the 72-50 player would be a worthy question to ask.

I agree. Unfortunately, the lower numbers the more "extreme" results. And the higher numbers, the less "extreme" results. But problem is that that rule continues to be true even for high numbers. The 40-13 case will still be slightly more vulnerable than the 72-50 case (I think, but that case it might be negligable).

Anyway, I don't like dividing GF by GA, because to me it only makes sense when
GF+GA is equally big for every player.
(But maybe there is something built in in overpass' method, that takes care of that.)

I look at it like this:
A: Player being 40-20 actually helped his team improve by +20.
B: Player being 30-15 actually helped his team improve by +15.
Both have the same GF/GA (2.0). But I think what matters is GF-GA.
Let's say B was 30-12 instead, raising his GF/GA to 2.5. That may make him look like a better player when looking at GF/GA. But he would have helped his team improve by +18.
During the whole season, I think a player's goal is to help their team improve by as many goals as possible, by getting as good GF-GA as possible.

I had to edit the part about (and with) the tables in my last post.
(I made a change before posting on the board, so that you would see if player played L, C, R, but that flawed the results, since some forwards played on more than one position, so I had to call all forwards F. If there is some guy playing both D and F, which is rare, the stats for that guy may be unreliable.)

plusminus, I'll try to address your concerns about the use of GF/GA ratios.

First, my adjusted plus-minus metric does not use the player's on-ice GF/GA ratio (R-ON) in the calculations. Only the difference is used, as in regular plus-minus.

The R-OFF ratio is used to calculate the team adjustment component, in conjunction with the sum of GA and GF. So the adjustment scales with the number of GF and GA, just as with regular plus-minus

I really don't think your concerns about the use of ratios apply to this metric. The ratios are useful for a quick overview of the on/off ice relationship of the player and team, but are incomplete without a measure of quantity. Adjusted plus-minus includes a measure of quantity.

plusminus, I'll try to address your concerns about the use of GF/GA ratios.

First, my adjusted plus-minus metric does not use the player's on-ice GF/GA ratio (R-ON) in the calculations. Only the difference is used, as in regular plus-minus.

Thanks for clarifying.

Quote:

The R-OFF ratio is used to calculate the team adjustment component, in conjunction with the sum of GA and GF. So the adjustment scales with the number of GF and GA, just as with regular plus-minus

I think I may understand. I think I perhaps need to try it out myself to be sure.

Quote:

I really don't think your concerns about the use of ratios apply to this metric. The ratios are useful for a quick overview of the on/off ice relationship of the player and team, but are incomplete without a measure of quantity. Adjusted plus-minus includes a measure of quantity.

OK.

Sorry if I may have gotten things wrong. I think I need to re-produce myself what you are doing, to be sure I've understood things right.

Below are what it looks like. I have only included players with GF+GA >= 20. (Expect even larger differences for the other players.)
I think the raw data I assembled and corrected should be near 100 % correct.
The rightmost column shows GF+GA per 60 minutes. I have divided all those values by league average, to make it easier to compare.

Highest:

Team

Name

pos

ESTOI

EStoi%

ESGFGA%

diff

ESGFGA

normESGFGAper60min

CAR

BRUNO ST. JACQUES

D

297

0.081

0.138

0.057

35

1.577

CHI

BURKE HENRY

D

250

0.065

0.094

0.029

29

1.552

ATL

ILYA KOVALCHUK

F

1153

0.305

0.379

0.074

130

1.509

NYR

REM MURRAY

F

398

0.105

0.155

0.050

44

1.479

EDM

MIKE COMRIE

F

910

0.241

0.328

0.086

100

1.470

CHI

ERIC DAZE

F

722

0.188

0.257

0.070

79

1.464

LA

ADAM DEADMARSH

F

265

0.071

0.106

0.035

29

1.464

COL

PETER FORSBERG

F

1091

0.288

0.419

0.131

119

1.459

BOS

JOE THORNTON

F

1285

0.340

0.433

0.093

140

1.458

ATL

KIRILL SAFRONOV

D

414

0.110

0.131

0.022

45

1.454

TOR

ALEXANDER MOGILNY

F

943

0.258

0.348

0.090

102

1.447

TOR

KAREL PILAR

D

245

0.067

0.089

0.022

26

1.420

BOS

GLEN MURRAY

F

1400

0.371

0.458

0.087

148

1.414

ATL

DANY HEATLEY

F

1164

0.308

0.359

0.051

123

1.414

NYI

ROMAN HAMRLIK

D

1281

0.355

0.460

0.106

134

1.400

PIT

MARIO LEMIEUX

F

1082

0.286

0.387

0.101

113

1.397

MTL

NIKLAS SUNDSTROM

F

384

0.098

0.129

0.031

40

1.394

PHO

LANDON WILSON

F

328

0.089

0.125

0.036

34

1.387

SJ

NICHOLAS DIMITRAKOS

F

244

0.065

0.089

0.023

25

1.371

BOS

MIKE KNUBLE

F

1061

0.281

0.334

0.053

108

1.362

Lowest:

Team

Name

pos

ESTOI

EStoi%

ESGFGA%

diff

ESGFGA

normESGFGAper60min

WAS

BRIAN SUTHERBY

F

554

0.146

0.096

-0.05

27

0.652

PIT

IAN MORAN

F

1053

0.278

0.175

-0.10

51

0.648

CGY

STEVE BEGIN

F

436

0.118

0.078

-0.04

21

0.644

STL

TYSON NASH

F

532

0.142

0.087

-0.05

25

0.629

TOR

RICHARD JACKMAN

D

535

0.146

0.085

-0.06

25

0.625

FLA

IGOR ULANOV

D

823

0.215

0.146

-0.07

38

0.618

MIN

JASON MARSHALL

F

462

0.119

0.084

-0.04

21

0.608

TB

ALEXANDER SVITOV

F

511

0.132

0.083

-0.05

23

0.602

CAR

JAROSLAV SVOBODA

F

549

0.150

0.095

-0.05

24

0.585

TOR

PAUL HEALEY

F

458

0.125

0.068

-0.06

20

0.584

BUF

VACLAV VARADA

F

525

0.139

0.082

-0.06

22

0.561

CGY

STEVE MONTADOR

D

627

0.170

0.096

-0.07

26

0.555

STL

SHJON PODEIN

F

540

0.144

0.073

-0.07

21

0.520

COL

SERGE AUBIN

F

700

0.185

0.095

-0.09

27

0.516

PIT

IAN MORAN

D

1053

0.278

0.134

-0.14

39

0.496

Biggest differences between real ES%, and ES% estimated by GF+GA:

Team

Name

pos

ESTOI

EStoi%

ESGFGA%

diff

ESGFGA

normESGFGAper60min

PIT

IAN MORAN

D

1053

0.278

0.134

-0.14

39

0.496

COL

PETER FORSBERG

F

1091

0.288

0.419

0.131

119

1.459

NYI

MATTIAS TIMANDER

D

1159

0.321

0.213

-0.11

62

0.716

NYI

ROMAN HAMRLIK

D

1281

0.355

0.460

0.106

134

1.400

PIT

MARIO LEMIEUX

F

1082

0.286

0.387

0.101

113

1.397

PHO

OSSI VAANANEN

D

1056

0.287

0.192

-0.10

52

0.659

PIT

IAN MORAN

F

1053

0.278

0.175

-0.10

51

0.648

STL

PAVOL DEMITRA

F

1151

0.308

0.406

0.098

116

1.348

TB

VINCENT LECAVALIER

F

1134

0.293

0.390

0.097

108

1.274

BOS

JOE THORNTON

F

1285

0.340

0.433

0.093

140

1.458

WAS

SERGEI GONCHAR

D

1584

0.417

0.509

0.092

143

1.208

TOR

ALEXANDER MOGILNY

F

943

0.258

0.348

0.090

102

1.447

CGY

STEPHANE YELLE

F

1054

0.285

0.200

-0.09

54

0.686

COL

SERGE AUBIN

F

700

0.185

0.095

-0.09

27

0.516

BOS

GLEN MURRAY

F

1400

0.371

0.458

0.087

148

1.414

EDM

MIKE COMRIE

F

910

0.241

0.328

0.086

100

1.470

COL

MILAN HEJDUK

F

1219

0.322

0.405

0.083

115

1.262

TB

MARTIN ST. LOUIS

F

1123

0.290

0.372

0.082

103

1.227

FLA

OLLI JOKINEN

F

1168

0.305

0.385

0.080

100

1.146

BOS

SEAN O'DONNELL

D

1150

0.305

0.229

-0.08

74

0.861

VAN

TODD BERTUZZI

F

1223

0.334

0.413

0.079

117

1.280

DET

MATHIEU DANDENAULT

D

1203

0.314

0.392

0.078

122

1.357

PHO

PAUL MARA

D

1129

0.307

0.384

0.077

104

1.233

FLA

IVAN NOVOSELTSEV

F

960

0.250

0.327

0.077

85

1.185

MIN

MARIAN GABORIK

F

1078

0.278

0.355

0.077

89

1.105

ATL

ILYA KOVALCHUK

F

1153

0.305

0.379

0.074

130

1.509

This makes, in my opinion, GF+GA a bit unreliable when using it to determine ice time. Maybe there are steps involved in the calculations that takes care of that, so that it really doesn't matter that much. But I felt a need to point it out.

To be honest, I think this reveals how effective a model that uses GF/GA can be.

they actaually do include an adjustment based on the line or pairing the player was on, because as you can see, goals are more frequent on a per-minute basis when the higher minute players are out there. So this will partially mitigate the effect that you're seeing, an effect that is pretty small to begin with.

I mean, if you want to try to approximate icetime across the board from 1967-onwards, be my guest. But can you improve on what exists enough that it is worth the time it would take?

As for Kovalchuk, considering two other Thrashers are in your top-20, he doesn't appear to really be that much of an outlier on his team. He just barely makes the bottom list that you provided, and only because it is based on a "raw" difference and not a percentage difference (if it was based on that, he would not be anywhere near the top)

Quote:

I agree. Unfortunately, the lower numbers the more "extreme" results. And the higher numbers, the less "extreme" results. But problem is that that rule continues to be true even for high numbers. The 40-13 case will still be slightly more vulnerable than the 72-50 case (I think, but that case it might be negligable).

Anyway, I don't like dividing GF by GA, because to me it only makes sense when
GF+GA is equally big for every player.
(But maybe there is something built in in overpass' method, that takes care of that.)

I look at it like this:
A: Player being 40-20 actually helped his team improve by +20.
B: Player being 30-15 actually helped his team improve by +15.
Both have the same GF/GA (2.0). But I think what matters is GF-GA.
Let's say B was 30-12 instead, raising his GF/GA to 2.5. That may make him look like a better player when looking at GF/GA. But he would have helped his team improve by +18.
During the whole season, I think a player's goal is to help their team improve by as many goals as possible, by getting as good GF-GA as possible.

Keep in mind that generally when we talk about r-on and r-ff we are talking about very large sample sizes - seasons at the very least, and generally blocks of seasons, or careers. Like you, I don't see any value in the micro aspect, these 10-20-game segments and single game scenarios you are providing.

overpass, as usual, did a much better job than I could have done, fuddling my way through descriptions of statistics in "normal people" words and terms.

SFrac: Season Fraction. 1.00 is a full season. I prefer it to games played because it gives a 48 game season, a 74 game season, an 80 game season or an 82 game season the same weight.$ESGF: Even-strength goals for, normalized to a 200 ESG scoring environment and with estimated SH goals removed.$ESGA: Even-strength goals against, normalized to a 200 ESG scoring environment and with estimated SH goals removed.R-ON: Even strength GF/GA ratio when the player is on the ice.R-OFF: Even-strength GF/GA ratio when the player is off the ice.XEV+/-: Expected even-strength plus-minus, which is an estimate of the plus-minus that an average player would post with the same teammates. The calculation is described above.EV+/-: Even –strength plus-minus, which is simply plus-minus with estimated shorthanded goals removed and normalized to a 200 ESG environment.AdjEV+/-: Adjusted even-strength plus-minus, which is even-strength plus-minus minus expected even-strength plus-minus. This is the final number.
The following three stats evaluate special teams play and are not related to adjusted plus-minus. I’m including them in the table for a quick reference to the player’s contributions outside of even-strength play.PP% : The % of the team’s power play goals for that the player was on the ice for.SH%: The % of the team’s power play goals against that the player was on the ice for.$PPP/G: Power play points per game, normalized to a 70 PPG environment and with pre-1988 PP assists estimated.

Results
Here are the top 60 in career adjusted even-strength plus-minus, as well as the players in the HOH Top 100 and several others who were strongly considered for voting.

If it had been named "$EV+/-", I would have been pretty sure it's $ESGF-$ESGA, because $ tells me that it's "adjusted to 200 ESG scoring environment".
My question is... Is EV+/- = $ESGF-$ESGA ?

The text also says:

Quote:

To calculate the adjusted plus-minus, I take the player’s on-ice total goals for and against as given. I calculate an expected plus-minus for the player, based on his team’s off-ice performance.

"As given", does that mean they are not "adjusted to 200 ESG scoring environment"?

Example, using made up seasonal stats for one player and his team.

Everything is ES only.
"without" or "w" means when player was off the ice.
GD (goal difference) = GF-GA.

Lge aver ESGF per team

teamGD

teamGF

teamGA

playerGD

playerGF

playerGA

withoutGD

withoutGF

withoutGA

pGF/pGA

wGF/wGA

100

+20

60

40

+10

24

14

+10

36

26

1.714

1.385

Lge aver ESGF per team

$teamGD

$teamGF

$teamGA

$playerGD

$playerGF

$playerGA

$withoutGD

$withoutGF

$withoutGA

pGF/pGA

wGF/wGA

200

+40

120

80

+20

48

28

+20

72

52

1.714

1.385

Are the $ values above true? Is that how the ""adjusted to 200 ESG scoring environment" values are calculated?

If the above is correct, then how do we use the different variables to calculate the missing columns?
R-On? R-Off?

Can someone write down the formula's for calculating the values, using the variables of the tables above?

And can we write "rOn" and "rOff" instead of "R-On" and "R-Off", to make it easier to understand the formulas? ("-" can otherwise be interpreted as a minus sign. But we don't take R minus On, and R minus Off, right? If, I'm even more confused.)

Quote:

The expected plus-minus is calculated using the off-ice performance regressed partially to even, as a player should be expected to play somewhat better than a set of bad teammates or worse than a set of good teammates.

I understand the regression thing. But I'm confused about other things, including what exactly to regress (I guess it's "wGF/wGA"). ? Is rOff = "wGF/wGA" regressed to even?

Quote:

I then calculate an actual plus-minus, which differs from official NHL plus-minus in that it is normalized to a scoring environment of 200 even-strength goal per season and does not include shorthanded goals. I subtract the “expected plus-minus” from the “actual plus-minus” to generate an adjusted plus-minus number.

If it had been named "$EV+/-", I would have been pretty sure it's $ESGF-$ESGA, because $ tells me that it's "adjusted to 200 ESG scoring environment".
My question is... Is EV+/- = $ESGF-$ESGA ?

The text also says:

"As given", does that mean they are not "adjusted to 200 ESG scoring environment"?

All numbers are adjusted to the 200 ESG per team-season scoring environment. Yes, EV+/- is simply $ESGF-$ESGA. "As given" still means scoring-adjusted numbers.

Quote:

Originally Posted by plusandminus

Example, using made up seasonal stats for one player and his team.

Everything is ES only.
"without" or "w" means when player was off the ice.
GD (goal difference) = GF-GA.

Lge aver ESGF per team

teamGD

teamGF

teamGA

playerGD

playerGF

playerGA

withoutGD

withoutGF

withoutGA

pGF/pGA

wGF/wGA

100

+20

60

40

+10

24

14

+10

36

26

1.714

1.385

Lge aver ESGF per team

$teamGD

$teamGF

$teamGA

$playerGD

$playerGF

$playerGA

$withoutGD

$withoutGF

$withoutGA

pGF/pGA

wGF/wGA

200

+40

120

80

+20

48

28

+20

72

52

1.714

1.385

Are the $ values above true? Is that how the ""adjusted to 200 ESG scoring environment" values are calculated?

All correct. I don't scoring-level adjust the off-ice numbers, since I only use them to calculate a ratio, but if you did want to adjust for scoring level that would be correct.

Quote:

Originally Posted by plusandminus

If the above is correct, then how do we use the different variables to calculate the missing columns?
R-On? R-Off?

Can someone write down the formula's for calculating the values, using the variables of the tables above?

And can we write "rOn" and "rOff" instead of "R-On" and "R-Off", to make it easier to understand the formulas? ("-" can otherwise be interpreted as a minus sign. But we don't take R minus On, and R minus Off, right? If, I'm even more confused.)

R-ON = $ESGF/$ESGA. For single seasons, multiple seasons, or careers.

R-OFF = (TeamESGF-PlayerESGF)/(TeamESGA-PlayerESGA) for a single season. For multiple seasons, take the sum of the XEV+/-, $ESGF, and $ESGA, and calculate by turning around the formula for XEV+/-

I understand the regression thing. But I'm confused about other things, including what exactly to regress (I guess it's "wGF/wGA"). ? Is rOff = "wGF/wGA" regressed to even?

I think I need an example to understand.

Adjusted plus-minus applies the regression to the ratio rOff in the XEV calculation. It's simply rOff^0.65, which regresses rOff toward 1. If I understand your terms correctly, wGF/wGA = rOff as I present it. I have never presented the regressed rOff value alone.

Full example:

Player X has 60 ESGF, 45 ESGA. His team has 140 ESGF, 155 ESGA. League scoring level is 150 ESGA/team.

OK, I post my results for 2002-03 season using overpass' formulas. I have not adjusted to era, since I only look at one season. I used .65 as the "regress to even" number. Let me know if numbers are wrong. (Please don't overfocus on the number of decimals shown. I want them there for verifying purposes.)

Lowest expected +/-:

Team

Pos

Name

TOIshare

+/-

+/- without player

rOn

rOff

exp+/-

adj+/-

PIT

F

MARIO LEMIEUX

0.2856

-15

-49

0.7656

0.5702

-20.4062

5.4062

CBJ

D

LUKE RICHARDSON

0.4065

-26

-41

0.6709

0.6204

-20.3193

-5.6806

CBJ

D

JAROSLAV SPACEK

0.3544

-19

-48

0.7206

0.5966

-19.4554

0.4554

ATL

F

DANY HEATLEY

0.3079

-1

-50

0.9839

0.6296

-18.3552

17.3552

PIT

F

ALEXEI KOVALEV

0.2415

-4

-60

0.9149

0.5420

-17.6831

13.6831

PIT

D

DICK TARNSTROM

0.2631

-7

-57

0.8600

0.5547

-17.5984

10.5984

CBJ

F

DAVID VYBORNY

0.2859

15

-82

1.5172

0.4810

-17.0432

32.0432

CBJ

F

GEOFF SANDERSON

0.2760

-1

-66

0.9767

0.5417

-16.7163

15.7163

PIT

F

MARTIN STRAKA

0.2428

-6

-58

0.8723

0.5573

-16.5250

10.5250

CAR

D

SEAN HILL

0.3440

5

-54

1.1471

0.5385

-14.4917

19.4917

(Comment: Dominated by Pittsburgh and Columbus players.)

Highest expected +/-:

Team

Pos

Name

TOIshare

+/-

+/- without player

rOn

rOff

exp+/-

adj+/-

COL

F

JOE SAKIC

0.2269

9

45

1.2500

1.5696

11.7839

-2.7839

PHI

D

ERIC WEINRICH

0.3580

15

30

1.3750

1.4688

11.8073

3.1926

PHI

D

KIM JOHNSSON

0.3605

16

29

1.3902

1.4603

11.9996

4.0004

DAL

D

RICHARD MATVICHUK

0.2767

-5

57

0.8611

1.8028

12.6784

-17.6784

COL

D

ROB BLAKE

0.3652

19

35

1.4524

1.4795

13.0408

5.9591

DAL

D

DERIAN HATCHER

0.4141

27

25

1.5870

1.4098

13.2289

13.7710

VAN

D

BRENT SOPEL

0.3782

-10

35

0.8246

1.4861

13.3167

-23.3168

COL

D

ADAM FOOTE

0.3842

27

27

1.5510

1.4091

13.8747

13.1252

DAL

D

SERGEI ZUBOV

0.3819

17

35

1.4048

1.5385

14.0487

2.9512

COL

F

STEVEN REINPRECHT

0.2496

-9

63

0.8125

1.9403

18.4572

-27.4572

COL

D

GREG DE VRIES

0.4051

16

38

1.2759

1.6667

21.7152

-5.7152

Comment: Some Colorado, some Philadelphia, some Dallas.

Best adjusted +/-:

Team

Pos

Name

TOIshare

+/-

+/- without player

rOn

rOff

exp+/-

adj+/-

COL

F

PETER FORSBERG

0.2885

55

-1

2.7188

0.9880

-0.4688

55.4688

COL

F

MILAN HEJDUK

0.3223

49

5

2.4848

1.0610

2.2119

46.7881

DET

D

NICKLAS LIDSTROM

0.3878

36

1

1.7500

1.0112

0.4793

35.5207

LA

F

ZIGMUND PALFFY

0.3235

24

-28

1.6316

0.7228

-10.5125

34.5125

PHO

F

LADISLAV NAGY

0.3002

25

-26

1.8929

0.7593

-7.2309

32.2309

COL

F

ALEX TANGUAY

0.3104

38

16

2.1875

1.1928

5.8372

32.1627

CBJ

F

DAVID VYBORNY

0.2859

15

-82

1.5172

0.4810

-17.0432

32.0432

DAL

F

JERE LEHTINEN

0.2803

33

19

2.4348

1.2262

5.2278

27.7722

STL

F

ERIC BOGUNIECKI

0.2453

24

-10

1.8889

0.9083

-2.4386

26.4385

BOS

F

MIKE KNUBLE

0.2811

22

-11

1.5116

0.9027

-3.5934

25.5934

PHO

F

DAYMOND LANGKOW

0.3225

19

-20

1.5588

0.8039

-6.1608

25.1607

MTL

D

ANDREI MARKOV

0.3408

18

-26

1.4865

0.7869

-7.1518

25.1517

Comment: Similar to the method I used and posted yesterday (post #184). Forsberg atop here too. Hejduk higher, as is Tanguay, which I think is not so good. Lidstrom higher. Vyborny lower, I think he should be higher, as I think +15 with vs -82 "without" is a huge difference. Palffy, Lehtinen, Boguniecki on my list too.
Martin St Louis, who was high on my list(s), is missing here. He's 25th here. Perhaps it has to do with how he distributed his ESGF and ESGF game by game.

Best adjusted (if not "regressing R-Off to even"):

Team

Pos

Name

TOIshare

+/-

+/- without player

rOn

rOff

exp+/-

adj+/-

COL

F

PETER FORSBERG

0.2885

55

-1

2.7188

0.9880

-0.7212

55.7212

COL

F

MILAN HEJDUK

0.3223

49

5

2.4848

1.0610

3.4023

45.5976

CBJ

F

DAVID VYBORNY

0.2859

15

-82

1.5172

0.4810

-25.58120

40.5812

LA

F

ZIGMUND PALFFY

0.3235

24

-28

1.6316

0.7228

-16.0919

40.0919

PHO

F

LADISLAV NAGY

0.3002

25

-26

1.8929

0.7593

-11.0842

36.0842

DET

D

NICKLAS LIDSTROM

0.3878

36

1

1.7500

1.0112

0.7374

35.26257

COL

F

ALEX TANGUAY

0.3104

38

16

2.1875

1.1928

8.9670

29.0330

MTL

D

ANDREI MARKOV

0.3408

18

-26

1.4865

0.7869

-10.9724

28.9724

NYI

D

ROMAN HAMRLIK

0.3548

16

-15

1.2712

0.8256

-12.8025

28.8025

PHO

F

DAYMOND LANGKOW

0.3225

19

-20

1.5588

0.8039

-9.4565

28.4565

STL

F

ERIC BOGUNIECKI

0.2453

24

-10

1.8889

0.9083

-3.7500

27.7500

BOS

F

MIKE KNUBLE

0.2811

22

-11

1.5116

0.9027

-5.5256

27.5255

ATL

F

DANY HEATLEY

0.3079

-1

-50

0.9839

0.6296

-27.9545

26.9545

CAR

D

SEAN HILL

0.3440

5

-54

1.1471

0.5385

-21.9000

26.9000

TB

D

DAN BOYLE

0.3600

13

-22

1.2889

0.7755

-13.0229

26.0229

Comment: At first glance it looks "better", in that linemates appear a bit more separated. But experience has shown me that regressing "when player off the ice" to even usually gives better results. (By the way, 6 Europeans atop.)

Although I like to compare the results to "my" mentioned method (see post #184), my method is not perfect. I need to find a way to include games where the player played but wasn't on the ice on any ES goals either way. Plus think more about it. Good things with it are that it doesn't need to pay attention to ice time, and doesn't have to adjust to "different GPG in different eras".

Now that I may know how overpass have done the calculations, and have been able to (hopefully) reproduce the results, my impression is that overpass' technique gives good results considered how relatively simple it is.
By simple, I mean that it only depends on ESGF and ESGA (and adjustment for ESGF per season), and that basically the only "tricky" part was the formula to calculate the expected +/-. That formula seem to produce interestingly good results.
(I did however not understand how it was done until it was written down in detail.)

The things I "don't like" about it, may be mostly present when looking at single seasons. When aggregating seasons, it might become alright (as players will play on other lines, on teams differently strong, etc). That is also what overpass have said.

Thanks overpass for explaining more in detail. It currently seems as if most of my "suspicions" regarding your method may have been a bit overstated.

Hopefully I will be able to reproduce czechyourmath's method too... eventually.

I have an alternative that might be fairer to players on great teams without using somewhat arbitrary regressions to the mean. It's not exactly comparable to adjusted plus-minus, but it uses much of the same methodology. For lack of a better term, I might call it "even strength value". It has two primary components:

1. Player's share of team success at even strength
2. Player's marginal (additional) success at even strength

this is the pythagorean win formula; N = 2 (or another number if supported by data)

Player's marginal contribution to team success is calculated as follows:

Subtract the player's ESGF and ESGA from the team's totals.
Recalculate the ES Win % from the new numbers (this is ES Win % without player).
Subtract Team Exp. ES Win % from ES Win % without player.
Multiply the difference in Win % by 82 to yield player's marginal contribution.

Then add player's share of team success ES and player's marginal contribution to team success at ES to get "ES Value" (whatever is proper term). The results are in the same ballpark as plus-minus.

Is the above still true? Or did you come up with changes to improve further?

Anyway, I tried to calculate according to how I interpreted the instructions, and below are my results for the 2002-03 season.
Columns starting with "x" is "without" player, i.e. teamStat - playerStat. GS = goal sum (GF+GA).
I haven't multiplied anything by 82. Should be OK anyway, right?

You are welcome to check my math for errors and/or misunderstandings.

Team

Pos

Name

GF

GA

GS

xGS

xGF

xGA

+/-

x+/-

playerWin

xWin

teamWin

pmargCont

Win

COL

F

PETER FORSBERG

87

32

119

109

82

83

55

-1

0.262331

0.286398

0.683506

0.419013

0.681344

COL

F

MILAN HEJDUK

82

33

115

103

87

82

49

5

0.247891

0.276771

0.683506

0.404928

0.652819

DAL

D

DERIAN HATCHER

73

46

119

79

86

61

27

25

0.204417

0.307920

0.688292

0.447368

0.651785

COL

D

ADAM FOOTE

76

49

125

81

93

66

27

27

0.194943

0.300838

0.683506

0.440139

0.635082

COL

D

GREG DE VRIES

74

58

132

70

95

57

16

38

0.168469

0.317685

0.683506

0.464787

0.633256

COL

F

ALEX TANGUAY

70

32

102

92

99

83

38

16

0.221417

0.245484

0.683506

0.359154

0.580571

WAS

D

SERGEI GONCHAR

80

63

143

32

68

70

17

-2

0.063001

0.281536

0.553229

0.508895

0.571896

DET

D

NICKLAS LIDSTROM

84

48

132

73

90

89

36

1

0.144899

0.262009

0.617310

0.424436

0.569335

DAL

D

PHILIPPE BOUCHER

60

38

98

74

99

69

22

30

0.191479

0.253581

0.688292

0.368420

0.559899

DAL

D

SERGEI ZUBOV

59

42

101

69

100

65

17

35

0.178541

0.261343

0.688292

0.379697

0.558238

PHI

D

KIM JOHNSSON

57

41

98

61

92

63

16

29

0.162122

0.260459

0.672411

0.387350

0.549472

COL

D

ROB BLAKE

61

42

103

73

108

73

19

35

0.175689

0.247891

0.683506

0.362675

0.538364

PHI

D

ERIC WEINRICH

55

40

95

60

94

64

15

30

0.159465

0.252486

0.672411

0.375493

0.534958

DAL

F

MIKE MODANO

55

30

85

77

104

77

25

27

0.199242

0.219942

0.688292

0.319547

0.518789

DAL

F

JERE LEHTINEN

56

23

79

85

103

84

33

19

0.219942

0.204417

0.688292

0.296991

0.516933

PHI

D

ERIC DESJARDINS

54

29

83

70

95

75

25

20

0.186042

0.220593

0.672411

0.328062

0.514104

OTT

D

WADE REDDEN

62

44

106

60

101

77

18

24

0.136208

0.240635

0.644722

0.373238

0.509446

BOS

F

GLEN MURRAY

83

65

148

29

84

91

18

-7

0.047945

0.244688

0.534016

0.458203

0.506148

DET

D

MATHIEU DANDENAULT

70

52

122

55

104

85

18

19

0.109170

0.242160

0.617310

0.392282

0.501452

COL

D

DEREK MORRIS

55

34

89

75

114

81

21

33

0.180503

0.214197

0.683506

0.313379

0.493882

Forsberg atop here too. But I think there are far too much Colorado dominance at the top. Basically, it seems to list the players with highest ESGF+ESGA on the teams.
We see some familiar names from the other two methods, like Hejduk, Lehtinen, Tanguay, but also many new.

Have I missed something in my calculations?

While I think "my" method and overpass' method ended up with quite similar results, I think this method gives the most "different" results. That does not necessarily have to bad, but looking at the table it does not seem to care much about "how good" the player played. Guys like Foote and DeVries don't look special +/- wise when comparing them to how Colorado did when they were off the ice.
The list is very much dominated by defencemen.
The only forwards on the list are: Forsberg-Hejduk-Tanguay, Modano-Lethinen and G.Murray. Among forwards will soon follow Bertuzzi-Naslund-Morrison (in between them are a few other forwards), all close to each other.

Shoudn't there be some consideration paid to GF-GA, or GF/(GF+GA), or even GF/GA?
Maybe I've missed something?

Edit: By the way, some guys ended up with slightly negative numbers. Is that OK?
Worst:

Team

Pos

Name

GF

GA

GS

xGS

xGF

xGA

+/-

x+/-

playerWin

xWin

teamWin

pmargCont

Win

CBJ

F

KENT MCDONELL

0

1

1

-68

120

186

-1

-66

-0.064606

0.000950

0.291681

0.003256

-0.061350

CBJ

F

MATHIEU DARCHE

0

1

1

-68

120

186

-1

-66

-0.064606

0.000950

0.291681

0.003256

-0.061350

Edit:

I experimented a bit more.
teamWin = team win formula
xWin = appplying win formula but with "without" stats instead of team stats. ("Without"=team-player.)
Then the differences between the two.
playerWin = applying win formula but with player stats instead of team stats. Gives strange results for players with low numbers.
The results below looks far "better" than the ones above.
One thing I suspect is still missing, is to add something more to it. I think we know below much "difference" the player did, but I think there might be something more added? (Perhaps something to do with (playerGF+playerGA) / (teamGF+teamGA)?? I'm very tired now, by will continue probably tomorrow.

Team

Pos

Name

GF

GA

GS

xGS

xGF

xGA

+/-

x+/-

teamWin

xWin

Diff

Diff%

playerWin

COL

F

PETER FORSBERG

87

32

119

109

82

83

55

-1

0.683506

0.493939

0.189567

1.383786

0.880833

COL

F

MILAN HEJDUK

82

33

115

103

87

82

49

5

0.683506

0.529559

0.153947

1.290707

0.860616

LA

F

ZIGMUND PALFFY

62

38

100

20

73

101

24

-28

0.485404

0.343142

0.142262

1.414586

0.726928

PHO

F

LADISLAV NAGY

53

28

81

24

82

108

25

-26

0.496310

0.365673

0.130637

1.357250

0.781797

DET

D

NICKLAS LIDSTROM

84

48

132

73

90

89

36

1

0.617310

0.505586

0.111724

1.220979

0.753846

CBJ

F

DAVID VYBORNY

44

29

73

-52

76

158

15

-82

0.291681

0.187898

0.103783

1.552336

0.697155

PHO

F

DAYMOND LANGKOW

53

34

87

18

82

102

19

-20

0.496310

0.392573

0.103737

1.264248

0.708448

NAS

D

JASON YORK

49

35

84

4

72

96

14

-24

0.460379

0.360000

0.100379

1.278830

0.662162

NYI

D

ROMAN HAMRLIK

75

59

134

17

71

86

16

-15

0.503436

0.405322

0.098114

1.242064

0.617724

STL

F

ERIC BOGUNIECKI

51

27

78

38

99

109

24

-10

0.548834

0.452033

0.096801

1.214145

0.781081

COL

F

ALEX TANGUAY

70

32

102

92

99

83

38

16

0.683506

0.587237

0.096269

1.163935

0.827143

TB

D

DAN BOYLE

58

45

103

4

76

98

13

-22

0.467543

0.375552

0.091991

1.244948

0.624234

MTL

D

ANDREI MARKOV

55

37

92

10

96

122

18

-26

0.474210

0.382406

0.091804

1.240069

0.688438

MIN

F

PASCAL DUPUIS

46

30

76

17

80

95

16

-15

0.503984

0.414910

0.089074

1.214682

0.701591

CAR

D

SEAN HILL

39

34

73

-44

63

117

5

-54

0.313326

0.224770

0.088556

1.393984

0.568173

LA

F

ALEXANDER FROLOV

49

33

82

12

86

106

16

-20

0.485404

0.396951

0.088453

1.222831

0.687965

DAL

F

JERE LEHTINEN

56

23

79

85

103

84

33

19

0.688292

0.600566

0.087726

1.146072

0.855661

BOS

F

MIKE KNUBLE

65

43

108

33

102

113

22

-11

0.534016

0.448970

0.085046

1.189424

0.695587

TB

F

MARTIN ST. LOUIS

57

46

103

2

77

97

11

-20

0.467543

0.386556

0.080987

1.209509

0.605591

STL

D

AL MACINNIS

69

50

119

33

81

86

19

-5

0.548834

0.470086

0.078748

1.167518

0.655694

Results looks much more similar to the other methods (those "by overpass" and "by me").

Dividing instead gives different results, see below. But those above are "better", right? ?

Team

Pos

Name

GF

GA

GS

xGS

xGF

xGA

+/-

x+/-

teamWin

xWin

Diff

Diff%

playerWin

CBJ

F

DAVID VYBORNY

44

29

73

-52

76

158

15

-82

0.291681

0.187898

0.103783

1.552336

0.697155

LA

F

ZIGMUND PALFFY

62

38

100

20

73

101

24

-28

0.485404

0.343142

0.142262

1.414586

0.726928

CAR

D

SEAN HILL

39

34

73

-44

63

117

5

-54

0.313326

0.224770

0.088556

1.393984

0.568173

COL

F

PETER FORSBERG

87

32

119

109

82

83

55

-1

0.683506

0.493939

0.189567

1.383786

0.880833

PHO

F

LADISLAV NAGY

53

28

81

24

82

108

25

-26

0.496310

0.365673

0.130637

1.357250

0.781797

COL

F

MILAN HEJDUK

82

33

115

103

87

82

49

5

0.683506

0.529559

0.153947

1.290707

0.860616

CBJ

F

GEOFF SANDERSON

42

43

85

-68

78

144

-1

-66

0.291681

0.226845

0.064836

1.285816

0.488236

PIT

F

ALEXEI KOVALEV

43

47

90

-68

71

131

-4

-60

0.290868

0.227051

0.063817

1.281069

0.455643

NAS

D

JASON YORK

49

35

84

4

72

96

14

-24

0.460379

0.360000

0.100379

1.278830

0.662162

FLA

D

ANDREAS LILJA

36

29

65

-31

75

120

7

-45

0.356902

0.280898

0.076004

1.270575

0.606457

PHO

F

DAYMOND LANGKOW

53

34

87

18

82

102

19

-20

0.496310

0.392573

0.103737

1.264248

0.708448

ATL

F

DANY HEATLEY

61

62

123

-52

85

135

-1

-50

0.354528

0.283889

0.070639

1.248826

0.491870

Last edited by plusandminus: 08-24-2011 at 06:47 PM.
Reason: adding more text

This is amazing stuff, very insightful! Do you have / are you willing to share the year-to-year spreadsheets? A friend of mine and I are trying to rank the best players since 1990, and this information would be very useful.

This is amazing stuff, very insightful! Do you have / are you willing to share the year-to-year spreadsheets? A friend of mine and I are trying to rank the best players since 1990, and this information would be very useful.

I don't fully endorse the single season plus-minus ratings as significant. There's a lot of random variation still at the season level. But I do find it useful for looking at groups of seasons like, say, Gretzky's Edmonton years compared to his LA years. Or for looking peak seasons (over several years) for any player.

I made the correction to prevent double counting of value. I have run some players' career ES Values with deductions for replacement level win% of 0, .125 and .250 (note: .250 is approx. the worst win% for non-expansion teams).

I'm not sure that even with a .250 team win% deduction (which is the most I would consider) it would really solve the issue of defensemen with long careers on good teams being possibly over-represented at the top of the list. One solution could be to separate d-men and forwards for comparison purposes. Another might be to use a player's ES points as a % of ESGF on-ice for, to give more talented offensive players their just due.

Wow, no Esposito. Is that an oversight or was he that one dimensional?